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Questions and Answers
Which process involves placing real numbers from smallest to largest along a horizontal number line?
Which process involves placing real numbers from smallest to largest along a horizontal number line?
What is the result of arranging real numbers in decreasing order?
What is the result of arranging real numbers in decreasing order?
If the numbers 3.7, 2.1, and 4.5 are arranged in increasing order, what sequence will be formed?
If the numbers 3.7, 2.1, and 4.5 are arranged in increasing order, what sequence will be formed?
What is the relationship between adjacent numbers when real numbers are arranged in decreasing order?
What is the relationship between adjacent numbers when real numbers are arranged in decreasing order?
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Which way of arranging real numbers involves listing the numbers from largest to smallest?
Which way of arranging real numbers involves listing the numbers from largest to smallest?
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What is the key characteristic of arranging real numbers in increasing order along a number line?
What is the key characteristic of arranging real numbers in increasing order along a number line?
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Study Notes
Arranging Real Numbers
Background Information
The real numbers, denoted as R, are numbers that extend the set of rational numbers using the square root of 2. They consist of finite and infinite sequences of digits, including rational numbers, irrational numbers, and special numbers such as 0 and ∞. The real number system provides a continuous range of values to model many physical phenomena.
Increasing Order
Arranging real numbers in increasing order involves placing the numbers from smallest to largest along a horizontal number line. On this line, every real number corresponds to a unique position, and the converse is also true. For example, if we have the numbers 1.2, 4.5, and 8.9, arranging them in increasing order would give us the sequence 1.2, 4.5, 8.9. In this case, each number lies to the right of the previous one on the real number line.
Decreasing Order
Arranging real numbers in decreasing order involves listing the numbers from largest to smallest along the horizontal number line. For example, if we have the same set of numbers as before - 1.2, 4.5, and 8.9 - arranging them in decreasing order would give us the sequence 8.9, 4.5, 1.2. Here, each number lies to the left of the subsequent one on the real number line.
In summary, when arranging real numbers, we can either place them in increasing order or decreasing order along the real number line. This allows us to compare and understand the relative magnitudes of different numbers within this numerical system.
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Description
Learn how to arrange real numbers in increasing or decreasing order along the real number line to compare their relative magnitudes. The real number system includes rational, irrational, and special numbers to model a continuous range of values in various phenomena.
